ALBANY — A union leader yesterday said Democratic Bill Thompson could have won Tuesday’s surprisingly close mayoral election if Gov. Paterson had backed an aggressive attack on Mayor Bloomberg.

Stuart Appelbaum, president of the Retail, Wholesale and Department Store Union, said he offered Paterson and state Democratic Chairman Jay Jacobs union funds to hire “a Howard Wolfson-like strong advocate” to take on Bloomberg, but that the offer was refused.

Wolfson was the sharp-tongued chief spokesman for Bloomberg’s campaign.

“I offered to pay for the position, but they abdicated their role . . . they didn’t do it,” said Appelbaum, who two months ago chided Paterson and Jacobs for allegedly being unwilling to take on Bloomberg.

“Bill Thompson wanted them to do this and if this had been done, the final result might have been different,” Appelbaum continued.

A spokesman for Paterson insisted the governor had forwarded Appelbaum’s offer to Jacobs.

Jacobs conceded Appelbaum offered to hire an aggressive party spokesman, but insisted, “I don’t know if I was even allowed to do that. To say we’re responsible or that we dropped the ball looks great today, but it isn’t the way I look at it.”